FAQs on Golden Rules of Solving Logarithm for CAT

Question 1

1. What are the golden rules for solving logarithm equations?

Accepted Answer

Ans. The golden rules for solving logarithm equations are as follows:1. Use the logarithmic properties to simplify the equation.2. Isolate the logarithmic term on one side of the equation.3. Apply the inverse operation of the logarithm to eliminate the logarithm.4. Solve the resulting equation for the variable.5. Check the solution to ensure it is valid in the original equation.

Question 2

2. What are the logarithmic properties used in solving logarithm equations?

Accepted Answer

Ans. The logarithmic properties commonly used in solving logarithm equations are:1. Product Rule: log(ab) = log(a) + log(b)2. Quotient Rule: log(a/b) = log(a) - log(b)3. Power Rule: log(a^b) = b * log(a)4. Change of Base Rule: log(a) = log(b) / log(c), where c is the desired base.

Question 3

3. How do you isolate the logarithmic term in a logarithm equation?

Accepted Answer

Ans. To isolate the logarithmic term in a logarithm equation, follow these steps:1. Remove any constants or coefficients from the logarithmic term by applying the logarithmic properties.2. Move any terms without logarithms to the other side of the equation.3. Ensure that there is only one logarithmic term on one side of the equation, with all other terms isolated on the other side.

Question 4

4. What is the inverse operation of the logarithm?

Accepted Answer

Ans. The inverse operation of the logarithm is exponentiation. If the logarithm of a number to a base is equal to another number, then raising the base to the power of the logarithm will give back the original number. For example, if log(base a) (x) = y, then a^y = x.

Question 5

5. Why is it important to check the solution in the original equation when solving logarithm equations?

Accepted Answer

Ans. It is important to check the solution in the original equation when solving logarithm equations because logarithms have certain restrictions. For example, the logarithm of a negative number or zero is undefined. Additionally, the base of the logarithm cannot be zero or one. Therefore, checking the solution ensures that it satisfies these restrictions and is a valid solution.

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